In　this　paper,　we　first　investigate　a　new　asymmetric　Huber　regression　(AHR)　estimation　procedure　to　analyze　skewed　data　with　partial　functional　linear　models.　To　automatically　reflect　distributional　features　as　well　as　bound　the　influence　of　outliers　effectively,　we　further　propose　a　weighted　composite　asymmetric　Huber　regression　(WCAHR)　estimation　procedure　by　combining　the　strength　across　multiple　asymmetric　Huber　loss　functions.　The　slope　function　and　constant　coefficients　are　estimated　through　minimizing　the　combined　loss　function　and　approximating　the　slope　function　with　principal　component　analysis.　The　asymptotic　properties　of　the　proposed　estimators　are　derived.　To　realize　the　WCAHR　estimation,　we　also　develop　a　practical　algorithm　based　on　pseudo　data.　Numerical　results　show　that　the　proposed　WCAHR　estimators　can　well　adapt　to　the　different　error　distributions,　and　thus　are　more　useful　in　practice.　Two　real　data　examples　are　presented　to　illustrate　the　applications　of　the　proposed　methods.